What mapping describes a rotation of 270 degrees clockwise about the origin?

To determine the mapping that represents a 270-degree clockwise rotation about the origin, it's essential to understand how points are transformed during such a rotation.

When a point ((x, y)) is rotated 270 degrees clockwise, it can be visualized as follows:

1. A 90-degree clockwise rotation transforms the point ((x, y)) to ((y, -x)).

2. A 180-degree clockwise rotation transforms the point ((x, y)) to ((-x, -y)).

3. A 270-degree clockwise rotation is equivalent to a 90-degree rotation counterclockwise, which transforms the point ((x, y)) to ((y, -x)).

Thus, the correct transformation for a 270-degree clockwise rotation about the origin is given by the mapping from ((x, y)) to ((y, -x)). This choice accurately reflects the nature of the transformation, ensuring that the point's orientation is correctly altered corresponding to the required angle of rotation.

Through this understanding, option C effectively describes the new position of the point after a 270-degree clockwise rotation, validating it as the correct choice.